Triangle Inequality
Do these side lengths form a triangle?
18, 22, 32.
Yes
Simplify: 7/√5
7√5/5
A right triangle, ∆RIA, ∠I is 90 degrees, and ∠R and ∠A are both 45 degrees. Side RI and side IA both measure as 7. What is the measure of side RA?
7√2
In ∆PMO, the measure of ∠O is 90°, PM=17, MO=15, and PO=8. What ratio represents the sine of ∠P?
15/17
In triangle RAT, ∠R is 12 degrees, ∠T is 20 degrees, and side AT measures as 16. What is the sine of ∠T? Round to the nearest hundredth.
26.32
Which is a Pythagorean triple?
A) 16, 22, 24
B) 14, 48, 50
C) 15, 25, 30
B) 14, 48, 50
Simplify: 4/√8
√2
A right triangle, ∆ZOE, ∠O is 90 degrees, ∠Z is 60 degrees, and ∠E is 30 degrees. Side ZO has a measure of 7√3 and side OE has a measure of 7. What is the measure of side EZ?
14
In ∆BOP, the measure of ∠O is 90°. BO=7 and PB=25. What is the measure of ∠B? (Round to the nearest whole number)
∠B=74°
In triangle MAP, side MA is 26, side AP is 13, and ∠A is 45 degrees. What is the length of the side MP? Round to the nearest whole number.
MP=19
In a right triangle, the side length of the hypotenuse is 37, and one of the legs is 12. What is the measure of the other leg?
35
Simplify: 5/2√3
5√3/6
In right triangle JOB, ∠O is 90 degrees, ∠B is 45 degrees, and side JB measures as 46. What is the measure of side JO?
Side JO= 23√2
In triangle DOG, ∠O is 90 degrees, side DO is 2.6 inches and side DG is 5.4 inches. What is the measure of ∠G? Round to the nearest hundredth.
∠G=28.78
In triangle XYZ side XY is 17.8, side YZ is 14.9, ∠X is 146 degrees, ∠Y is 22 degrees, and ∠Z is 12 degrees. What is the length of side XZ? Round to the nearest whole number.
Side XZ=32
The side lengths are 6, 24, and 26. What type of triangle does it form?
Obtuse triangle.
Simplify: 2/√18
√2/3
In right triangle, FUN, ∠U is 90 degrees, ∠F is 30 degrees, and the shorter leg of the triangle, UF, measures as 2. What is the measure of the 2nd leg and the hypotenuse?
2nd leg= 2√3
Hypotenuse= 4
In triangle CAT, ∠T is 90 degrees, side TA is 15.7 inches, side TC is 13.2 inches. What is the measure of ∠A? Round to the nearest whole number.
∠A=40 degrees
In triangle ABC side AB is 17, side BC is 14, side AC is 23, and ∠B is 74 degrees. What is the measure of ∠A? Round to the nearest whole number.
∠A=36
The side lengths are 6, 19, and 27, what type of triangle is it?
It's not a triangle.
Simplify: 7/2√3
7√3/6
In right triangle, HEY, ∠E is 90 degrees, ∠H is 30 degrees, and the shorter leg of the triangle HE measures 6√3. What are the lengths of the 2nd leg of the triangle and the hypotenuse?
2nd leg= 18
Hypotenuse= 12√3
Momo was chasing Zoe in a right triangle route (∆ABC) ∠B is 90 degrees, and ∠C is 36 degrees. Side BC is 8. What is the length of the longest route? (Round to the nearest tenth)
9.9
In triangle MOP side MO is 15, side OP is 13, and side MP is 26. What is the measure of ∠P? Round to the nearest whole number.
∠P=70